I have taken introductory courses on groups, rings, fields and vector spaces and am currently taking one on modules. A common theme among such subjects are the three isomorphism theorems (as in, those found here http://en.wikipedia.org/wiki/Isomorphism_theorems).
The naming of these theorems as "The First Isomorphism Theorem", "The Second Isomorphism Theorem" and "The Third Isomorphism Theorem" implies that they are in some way fundamental, basic theorems.
My question is, and I hope it's not too vague, in what sense are they fundamental and/or basic? Is it possible to formulate other, similar theorems, and if so, why would/are they not be grouped into this group of isomorphism theorems? I'm just trying to get a grasp of the big picture here.